WEST PALM BEACH, Fla. — Robert Gsellman won the Mets’ confidence late last summer and has done nothing to relinquish it this spring.

With a week remaining in the exhibition season, the competition for the fifth spot in the team’s rotation is officially open, but signs point to Gsellman on the brink of getting the job, at least to begin the season.

Zack Wheeler is still searching for consistency after spending two years rehabbing from Tommy John surgery and Seth Lugo had early success in the World Baseball Classic, but intrigues team officials as a potential answer in the bullpen, leaving Gsellman as your front-runner headed toward the finish line.

The right-hander aced another spring test Thursday, when he allowed only an unearned run over 5 1/3 innings against the Nationals, in the Mets’ 1-0 loss at The Ballpark of the Palm Beaches. In five appearances this spring, Gsellman has pitched to a 1.56 ERA.

“Hard work pays off and you take it on the field,” Gsellman said after a 79-pitch outing. “I throw 100 [pitches] and I’m ready to go.”

That final Grapefruit League appearance for Gsellman is expected to come Wednesday. And with team brass hesitant to consider Gsellman for a bullpen role, it’s likely Mets rotation or bust for him. In this case, bust would be starting the season at Triple-A Las Vegas.

“He is really showing that he belongs here, with the stuff, the great movement on the fastball, great poise on the mound, great demeanor the way he goes about things,” manager Terry Collins said. “So he’s going to be pretty good.”

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Wheeler had a rough outing a day earlier, tapering the enthusiasm he created last week when he was firing 97-mph missiles in this ballpark. In three appearances this spring, Wheeler has an 8.59 ERA, reason for Mets officials to take pause and wonder if he might benefit from extended spring training. Team officials have not ruled out the bullpen for Wheeler, but are hesitant to go that route with him given that he’s never previously worked as a reliever.

Lugo, who is expected to pitch in a split-squad game on Monday after taking the loss for Puerto Rico in the WBC finals against the United States, arrived to the major leagues as a reliever after shifting to the bullpen at Triple-A Las Vegas. The Mets view him as a potential middle-inning bridge in the bullpen if he’s not selected to the rotation.

Too many potential starting pitching options is a luxury for a manager, but it’s clear Collins would rather have his rotation set.